This paper considers the influence of circumferential wall heat conduction for the case of forced convection around a circular cylinder in cross flow of air. Keeping uniform heat generation from the inner surface of the cylinder in radial direction, heat is transferred by wall conduction in the circumferential direction due to the asymmetric nature of the temperature distribution of the cylinder and by convection around the perimeter of the cylinder. The wall conduction depends on conductivity of the cylinder and size of the cylinder radius and thickness and affects the local convective heat transfer rate significantly for geometrically similar surfaces and flow conditions. A nondimensional conjugation parameter K. (=k$_t$R/k$_w$b) has been used to characterize the effect of the circumferntial wall heat conduction. The small values of conjugation parameter K are found to be associated with large effect of wall conduction on the local convective heat transfer rate.